Question 3 required?d)Find the pdf of Y.e) Find the cdf of Y.3. A branch of a certain bank in New York City has six ATMs. Let Xrepresent the number of machines in use at a particular time of day.The edf of X is as follows:F(x)=0 ifx < 00.06 if0 3)(111) P(2 ≤X ≤5)(iv) P(2 < X<5).b) Find the pmf of X.4. The probability distribution of the amount of memory X (GB) in apurchased flash drive is given below.21p(x) 0.05 0.101S0.35 0.40160.10Compute the following: E(X). E(X), V(X). E3X-2). E(3X²-2). V(3X+2). E(X+1), V(X-1)

Answered: 3. A branch of a certain bank in New…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Related questions

Question

Question 3

required?
d)
Find the pdf of Y.
e) Find the cdf of Y.
3. A branch of a certain bank in New York City has six ATMs. Let X
represent the number of machines in use at a particular time of day.
The edf of X is as follows:
F(x)=
0 ifx < 0
0.06 if0<x<l
0.19 ifl ≤x<2
0.39 if2<x<3
0.67 if3 <x<4
0.92 if4 <x<5
0.97 if5 ≤x<6
ifx 26
T
a) Calculate the following probabilities directly from the cdf:
(1) p(2)
(11) P(X> 3)
(111) P(2 ≤X ≤5)
(iv) P(2 < X<5).
b) Find the pmf of X.
4. The probability distribution of the amount of memory X (GB) in a
purchased flash drive is given below.
2
1
p(x) 0.05 0.10
1
S
0.35 0.40
16
0.10
Compute the following: E(X). E(X), V(X). E3X-2). E(3X²-2). V(3X
+2). E(X+1), V(X-1)

Expert Solution

Step 1

As we are entitled to solve one question at a time, I will answer 2nd one as some information is missing in the first question, please submit other questions one at a time to get them answered.

Given information:

$F (x) = \{\begin{cases} \begin{matrix} 0; x < 0 \\ 0.06; 0 \leq x < 1 \\ 0.19; 1 \leq x < 2 \end{matrix} \\ \begin{matrix} 0.39; 2 \leq x < 3 \\ 0.67; 3 \leq x < 4 \\ 0.92; 4 \leq x < 5 \\ 0.97; 5 \leq x < 6 \\ 1; x \geq 6 \end{matrix} \end{cases}$